Depends when you get hit. I am best with advent imo but i'm really enjoying Vasari. That being said...as advent I always get carriers up ASAP as most people opt for missle frigs at the start. Once I have the number of carriers I feel comfortable with I begin building illums. Control the skies and you will iwn 99% of the time. I also put some flak in there to ensure the air is mine.
As Vasari, the best way to counter would be to match carriers with advent and have some flak and adjust accordingly....If you are up against say 7 carriers, 15 illums 8 flak and 4 guardians I would probobly use this fleet.
10 carriers, 8 flak, 4-5 overseers and either 15 assailants or tech to HC's if possible and pick up 7-8. Now I'm not sure how close this is resource to resource but I would start my fight with killing his illums with my fighters (my flak will kill his fighters eventually and vice versa so I want to get some use out of my fighters before that time. I would say my fighters would kill at least half his illums. I would keep my assailants in a different grav well until some of his fighters were down as well. Obviously if you can have a larger flet than him it would be ideal but a balanced advent fleet is a tough nut to crack.
My end game advent fleet usually consists of 7-10 carriers, 5-7 guardians, Mothership and Radiance (especially against TEC's Marza) 10-15 illums, 10-15 destra's and 3-5 subjugators, 6-10 flak and 10-15 disciples with the anti-matter stealing ability to take down carriers. All of this depends on your opponents fleet though....if he has spammed missle frigs I wouldnt build a single disciple until those are killed and no longer a threat...I hate wasting resources and I play my games as if it's a battle of attrition. Build your fleets to counter the enemty....if it's balanced, go for his greatest weakness (a lot of the time that would be heavy cruisers as they work well against everything).